We prove a version of the Doob Meyer decomposition for supermartingales with a linearly ordered index set. Key words Doob Meyer decomposition, natural increasing processes, potentials, supermartingales. Mathematics Subject Classi…cation (2000): : 28A12, 60G07, 60G20.

Although wavelet analysis is a relatively young mathematical subject, it has already drawn a great deal of attention, not only among mathematicians themselves, but from various other disciplines as well. In fact, it is fair to attribute the main driving force of the rapid development of this field to the “users” rather than to the “inventors” of mathematics. To the mathematicians, Fourier analy...

In the theory of wavelet frames, known Daubechies bases have been generalized to compactly supported (Daubechies-like) while bandlimited Meyer not date. this study, we will generalize basis into non-separable Meyer-like frames. By using a characteristic function mask Fourier transform one-dimensional scaling with width parameter, can produce family frame functions and associated After that, by ...